MSThE04
Curves and Surfaces in Computer Aided Geometric Design  Part III of III
For Part I, see MSThBC04
For Part II, see MSThD04
Date: August 13
Time: 16:0018:00
Room: 308
(Note: Click title to show the abstract.)
Organizer:
Jia, Xiaohong (Chinese Acad. of Sci.)
Cheng, JinSan (Chinese Acad. of Sci.)
Abstract: The symposium is aimed at bridging between people who are working theoretically on curves and surfaces in algebraic geometry and those who are endeavoring to seek for suitable modeling forms of curves and surfaces in Computer Aided Geometric Design. Therefore, the symposium includes wideranging topics on curves and surfaces from classic theory aspects to their applications in modern industry. The forms of curves and surfaces consist of but are not limited to: algebraic curves and surfaces, parametric curves and surfaces including NURBS as well as triangular surface patches.
MSThE041
16:0016:30
How Many Regions Does a Real Algebraic Curve Divide the Plane?
Cheng, JinSan (Chinese Acad. of Sci.)
Abstract: In this talk, we investigate the number of regions of a real algebraic plane curve C defined by f(x,y) = 0 dividing the real plane R^2. We obtain a relationship between the zeroth Betti number of R^2\C and the number of bounded connected components of C, from which we derive a formula only involved with f(x,y) for the zeroth Betti number. It is a joint work with Mingbo Zhang.
MSThE042
16:3017:00
An algebraic approach of computing the variations of the intersection curve of two moving quadrics
Jia, Xiaohong (Chinese Acad. of Sci.)
Abstract: We propose a symbolic algorithm for detecting the variations in the topological and algebraic properties of the intersection curve of two quadratic surfaces (QSIC) that are moving or deforming in PR3PR3 (real projective 3space). The core of our algorithm computes all the critical instants when the QSIC changes type using resultants and Jordan forms. These critical instants partition the time axis into intervals within which the QSIC is invariant. The QSIC at the computed critical instants and within the time intervals can both be exactly determined using symbolic technique. Examples are provided to illustrate our algorithm.
MSThE043
17:0017:30
Quaternion rational surfaces: Rational surfaces generated from the quaternion product of two rational space curves
Wang, Xuhui (Hefei Univ. of Tech.)
Abstract: A quaternion rational surface is a surface generated from two rational space curves by quaternion multiplication. The goal of this talk is to demonstrate how to apply syzygies to analyze quaternion rational surfaces. We show that we can easily construct three special syzygies for a quaternion rational surface from a $\mu$basis for one of the generating rational space curves. The implicit equation of any quaternion rational surface can be computed from these three special syzygies and inversion formulas for the nonsingular points on quaternion rational surfaces can be constructed. Quaternion rational ruled surfaces are generated from the quaternion product of a straight line and a rational space curve. We investigate special mubases for quaternion rational ruled surfaces and use these special mubases to provide implicitization and inversion formulas for quaternion rational ruled surfaces. Finally, we show how to determine if a real rational surface is also a quaternion rational surface.
MSThE044
17:3018:00
Geometric iteration method and its applications in geometric design
Hongwei, Lin (Zhejiang Univ.)
Abstract: Geometric iteration method, also called progressiveiterative approximation, is an iterative method with clear geometric meaning. By adjusting the control points of curves or surfaces iteratively, the limit curve or surface interpolates (approximates) the given data point set. In this report, we present the iterative formats of the interpolatory and approximating geometric iteration methods, show their convergence and local property, and develop the accelerating techniques. Moreover, some successful applications of the geometric iteration method are demonstrated.
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Footnote: Code: TypeDateTimeRoom No.
Type : IL=Invited Lecture, SL=Special Lectures, MS=Minisymposia, IM=Industrial Minisymposia, CP=Contributed Papers, PP=Posters
Date: Mo=Monday, Tu=Tuesday, We=Wednesday, Th=Thursday, Fr=Friday
Time : A=8:309:30, B=10:0011:00, C=11:1012:10, BC=10:0012:10, D=13:3015:30, E=16:0018:00, F=19:0020:00, G=12:1013:30, H=15:3016:00
Room No.: TBA
